Higher Spin vs. Renormalization Group Equations

TL;DR

This paper explores the connection between renormalization group equations and higher spin equations in a 3D scalar field theory, demonstrating their equivalence at classical and quantum levels under certain conditions.

Contribution

It shows that classical RG equations can be viewed as a variant of Vasiliev higher spin equations, extending this equivalence to quantum theory in the large N limit.

Findings

Classical RG equations are related to higher spin equations with Kleinians on AdS4.

The equivalence extends to the quantum theory away from fixed points in the large N limit.

The work provides a new perspective on the relationship between RG flows and higher spin theories.

Abstract

We present a variation of earlier attempts to relate renormalization group equations to higher spin equations. We work with a scalar field theory in 3 dimensions. In this case we show that the classical renormalization group equation is a variant of the Vasiliev higher spin equations with Kleinians on AdS$_4$ for a certain subset of couplings. In the large N limit this equivalence extends to the quantum theory away from the conformal fixed points.